Find the minimum value of the objective function and where it occurs,subject to the constraints: ?
Objective function:
?
Z = 8x + y
?
Constraints:
?
X ? 0
Y ? 0
X + 4y ? 20
X + y ? 18
?2x + 2y ? 21
?
A)Minimum at (0,0): 0
B)Minimum at (5,0): 40
C)Minimum at $$\left( \frac { 21 } { 2 } , 0 \right)$$ : 84
D)Minimum at (18,0): 144
E)No minimum

Question

Quizplus · Accepted Answer

The minimum value of the objective function Z = 8x + y occurs at the origin (0,0) because all constraints are satisfied at this point, and since both x and y are non-negative (X ≥ 0, Y ≥ 0), the smallest value Z can take is 0 when both x and y are 0.

Find the Minimum Value of the Objective Function and Where (212,0)\left( \frac { 21 } { 2 } , 0 \right)(221​,0)

Find the Minimum Value of the Objective Function and Where $\left( \frac { 21 } { 2 } , 0 \right)$